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(a). Write the instantaneous currents across the three circuit elements in terms of Vm amp > angular frequency @, inductance L, and capacitance C. (b). Relate for the ratio of the rms voltage and current towards the ratio of the amplitude voltage and current. (c). By using part (a) and (b), as well as the phasor diagram as guides, show that the rms current delivered by the source is 1 I =V. R? rms ms @L

(a). Write the instantaneous currents across the three circuit elements in terms of Vm amp > angular frequency @, inductance L, and capacitance C. (b). Relate for the ratio of the rms voltage and current towards the ratio of the amplitude voltage and current. (c). By using part (a) and (b), as well as the phasor diagram as guides, show that the rms current delivered by the source is 1 I =V. R? rms ms @L

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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3. Aside from the typical RLC circuit arranged in series, there exist that arranged in parallel as well (see Figure 3). In this configuration, the instantaneous voltages (and rms voltages) across each of the three circuit elements are the same, and each is in phase with the current in the resistor. The currents in C and L lead or lag the current in the resistor as shown in the phasor diagram (Figure 3b). By taking the instantaneous voltage across the AC source sin ot and the instantaneous current provided by the AC source to be to be v(t)=V, amp i(t) = 1mp sin (ot – ø) , where Vmp and Imp are the voltage and current amplitudes %3D amp respectively, (a) (b) AV Ic R. |AV. rms R Figure 3: (a) RLC circuit in parallel configuration and (b) phasor diagram for the RLC circuit. (a). Write the instantaneous currents across the three circuit elements in terms ofV. amp > angular frequency @, inductance L, and capacitance C. (b). Relate for the ratio of the rms voltage and current towards the ratio of the amplitude voltage and current. (c). By using part (a) and (b), as well as the phasor diagram as guides, show that the rms current delivered by the source is 1 +| @C• R? 1 I. = V rms 1 rms @L (d). By using part (a) and (b), as well as the phasor diagram as a guide, show that the phase angle ø between V. and Ims is given by rms 1 tan ø = R| 1 Xc X,
Transcribed Image Text:3. Aside from the typical RLC circuit arranged in series, there exist that arranged in parallel as well (see Figure 3). In this configuration, the instantaneous voltages (and rms voltages) across each of the three circuit elements are the same, and each is in phase with the current in the resistor. The currents in C and L lead or lag the current in the resistor as shown in the phasor diagram (Figure 3b). By taking the instantaneous voltage across the AC source sin ot and the instantaneous current provided by the AC source to be to be v(t)=V, amp i(t) = 1mp sin (ot – ø) , where Vmp and Imp are the voltage and current amplitudes %3D amp respectively, (a) (b) AV Ic R. |AV. rms R Figure 3: (a) RLC circuit in parallel configuration and (b) phasor diagram for the RLC circuit. (a). Write the instantaneous currents across the three circuit elements in terms ofV. amp > angular frequency @, inductance L, and capacitance C. (b). Relate for the ratio of the rms voltage and current towards the ratio of the amplitude voltage and current. (c). By using part (a) and (b), as well as the phasor diagram as guides, show that the rms current delivered by the source is 1 +| @C• R? 1 I. = V rms 1 rms @L (d). By using part (a) and (b), as well as the phasor diagram as a guide, show that the phase angle ø between V. and Ims is given by rms 1 tan ø = R| 1 Xc X,
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